This guy is not in LA, but he is a thyroid expert and he helped me when I needed it.
http://www.uchsc.edu/sm/endo/ridgway.php
I had my thyroid removed a few years ago and needed a second opinion. I was absolutely blown away at the amount of time this doc and his staff spent on my case.
If you can't swing visiting a doc outside of LA, I'd recommend going to a research hospital like the one above (UCLA?). In my limited experience, the research hospital spent 3x the time than a "regular" doc going over ALL the options.
Best of luck,
Martin